Riesz bases and positive operators on Hilbert space

James R. Holub

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-2

Abstract:

It is shown that a normalized Riesz basis for a Hilbert space H (i.e., the isomorphic image of an orthonormal basis in H ) induces in a natural way a new, but equivalent, inner product on H in which it is an orthonormal basis, thereby extending the sense in which Riesz bases and orthonormal bases are thought of as being the same . A consequence of the method of proof of this result yields a series representation for all positive isomorphisms on a Hilbert space.

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:468907

DOI: 10.1155/S0161171203202349

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